
<html lang="en">
 <head>
<title>Cindy JS Example</title>
<meta charset="UTF-8">
<script type="text/javascript" src="../build/js/Cindy.js"></script>
   </head> 
  <body style="font-family:Arial;">
        
        <h1>Schnitte durch 4-dimensionale reguläre Polytope</h1>

<div style="width:800px; line-height: 1.5">
Polytoptyp aussuchen und am Schieberegler eine 3-dimensionale Schnittebne festlegen.     
</div>
<br>
<br>

        <script id="init" type="text/x-cindyscript">

oldangle=120°;


wx=0;
wy=0;
oldparamv=(0,0,0,0,0);
oldcolparams=(0,0);

choice=3;
multicol=1;
next():=(choice=choice+1;if(choice==5,choice=1));
anim=false;

scal=0.15;

init=0;


mat=[ 
  [1,0,0],
  [0,1,0],
  [0,0,1]
];

mat0=[
  [1,0,0],
  [0,1,0],
  [0,0,1]
];



mmmx=mat0;
mmmy=mat0;





edgecol=(0.76,0.78,0.54);
edgecol=(.9,.9,.9);
edgecol=(0.4,0.3,0.3);

//Das Malt einen Punkt aus homogenen Koordinaten
renderPoint(p):=(
  pp=mat*p;
  draw((pp_1,pp_2),color->edgecol,border->false,size->3)
);

//Das Malt ein Segment aus homogenen Koordinaten
renderLine(p,q):=(
  pp=mat*p;
  qq=mat*q;
  draw((pp_1,pp_2),(qq_1,qq_2));
);




norm(p):=(p_1,p_2,p_3);




renderPolygon(pol,col):=(
//  pp=apply(pol,mat*#);

pp=pol;
  aa=pp_1;bb=pp_2,cc=pp_3;
  nn=cross(bb-aa,bb-cc);
  nn=nn/abs(nn);
  rgb=ambient;
 
  forall(lights,(
      shade=-sin(nn*#_1);
      if(nn*#_1>0,shade=0);
      rgb=rgb+#_2*shade;
    )
  );
  pp=apply(pp,(#_1,#_2));
  aa=pol_1;bb=pol_2,cc=pol_3;

  fillpoly(pp,color->(rgb_1*col_1,rgb_2*col_2,rgb_3*col_3),alpha->.8);
  connect(pp++[pp_1],color->(1,1,1)*sum(col)*.5,size->1);
//draw(center(pp),(nn_1,nn_2)*1+center(pp),color->(1,1,1));
);

renderPolygonB(pp,col):=(
//  pp=apply(pol,mat*#);

  aa=pp_1;bb=pp_2,cc=pp_3;
  nn=cross(bb-aa,bb-cc);
  nn=nn/abs(nn);
  rgb=ambient;
  forall(lights,(
      shade=-sin(nn*#_1);
      if(nn*#_1>0,shade=0);
      rgb=rgb+#_2*shade;
    )
  );
  pp=apply(pp,(#_1,#_2));

  fillpoly(pp,color->(rgb_1*col_1,rgb_2*col_2,rgb_3*col_3),alpha->alpha);
  connect(pp++[pp_1],color->(1,1,1)*sum(col)*.5,size->1);
//draw(center(pp),(nn_1,nn_2)*1+center(pp),color->(1,1,1));
);

renderPolygonF(pp,col):=(
//  pp=apply(pol,mat*#);
  aa=pp_1;bb=pp_2,cc=pp_3;
  nn=cross(bb-aa,bb-cc);
  nn=nn/abs(nn);
  rgb=ambient;
 
  forall(lights,(
      shade=-sin(nn*#_1);
      if(nn*#_1>0,shade=0);
      rgb=rgb+#_2*shade;
    )
  );
  pp=apply(pp,(#_1,#_2));

  fillpoly(pp,color->(rgb_1*col_1,rgb_2*col_2,rgb_3*col_3),alpha->alpha);
  
  border=pp++[pp_1];
  if(length(border)>3,
    apply(1..(length(border)+1),i,
      draw(border_i,border_(i+1),color->(1,1,1)*sum(col)*.5,size->2)
    );
   ); 
//  connect(pp++[pp_1],color->(1,1,1)*sum(col)*.5,size->3);
//draw(center(pp),(nn_1,nn_2)*1+center(pp),color->(1,1,1));
);









renderPolygonX(pol,col):=(
//  pp=apply(pol,mat*#);

pp=pol;
  pp=apply(pp,(#_1,#_2));
  fillpoly(pp,alpha->1);
);


//////////////////////////////////////////////////////


init3d():=(
// renderlist=[];
// pr=[];
);

center(ll):=sum(ll)/length(ll);


poly3d(l):=(l);



draw3d(a,b):=();


pro(vert):=(vert_1,vert_2,1);

ori(pol):=(
  det(pro(pol_1),pro(pol_2),pro(pol_3))
);

render3d():=(
mati=transpose(mat);
//err("B1 "+seconds());
  if(init==0,

//err("LONG "+seconds());
  renderlist=
  apply(pr,ll,
    mll=apply(ll_1,mat*(#))/scal;
    [mll,center(mll)_3,ll_2]   
  );    
  init=1;
  ,
//err("SHORT "+seconds());
  ii=1;

  forall(pr,ll,
    mll=ll_1*mati/scal;

    (renderlist_ii)_1=mll;
    (renderlist_ii)_2=center(mll)_3;
    (renderlist_ii)_3=ll_2;
      ii=ii+1;
  );    



);

//err("B2 "+seconds());

//  rl=sort(renderlist,#_2);

//err("B3 "+seconds());
  forall(renderlist,pol,
      if(ori(pol_1)~>=0,
       renderPolygonB(pol_1,pol_3*(pol_2+10)/10)   
      );
  );


 forall(renderlist,pol,
      if(ori(pol_1)~<=0,
       renderPolygonF(pol_1,pol_3*(pol_2+10)/10)   
      );
  ) ;
 

//err("B4 "+seconds());

);



///////////////////////////////////////////////////


//berechnet innkugel und umkugelradius

minmax(obj):= (
 if(length(obj)>3,
  ch=convexhull3d(obj);
  obj=ch_1;
  maxval=1/(-sort(apply(ch_1,-|#|))_1);
  ff=ch_2;
  dual=apply(ff,f,
    linearsolve((obj_(f_1),obj_(f_2),obj_(f_3)),(1,1,1));
  );
  ch=convexhull3d(dual);
  minval=-sort(apply(ch_1,-|#|))_1;
  (minval,maxval);
  ,
  (|obj_1|,|obj_1|);
 );
);


perm(a,b,c):=(
  (a,b,c),
  (a,c,b),
  (b,a,c),
  (b,c,a),
  (c,a,b),
  (c,b,a)
);


perm1(a,b,c):=(
  (a,b,c),
  (b,c,a),
  (c,a,b)
);




matrz(w):=(
(cos(w),sin(w),0),
(-sin(w),cos(w),0),
(0,0,1)
);

matrx(w):=(
(1,0,0),
(0,cos(w),sin(w)),
(0,-sin(w),cos(w))
);

matry(w):=(
(cos(w),0,-sin(w)),
(0,1,0),
(sin(w),0,cos(w))
);




nn(v):=v/|v|;






definebody(zell):=(
  body=zell_1;
  segs=zell_2;
  rf1=zell_3;
  rf2=zell_4;
  rf3=zell_5;
  rf4=zell_6;
);





colorf(obj,ff):=actcol;
colorf(obj,ff):=(
nn=linearsolve((obj_(ff_1),obj_(ff_2),obj_(ff_3)),(1,1,1));

nn=nn/|nn|;
//err(nn*initdirs_1);
//err(ff);
dd=-sort(apply(initdirs,-#*nn))_1;
//err(dd);
hue(colspan*spanfactor_(choice+1)_tchoice*(1-dd)+angle/(2*pi));
);


colorfx(obj,ff):=(
nn=linearsolve((obj_(ff_1),obj_(ff_2),obj_(ff_3)),(1,1,1));

hue(4*1/|nn|);
);



 object(obj,faces):=(
      pr= apply(faces,fa,[apply(fa_1,obj_#),fa_2])
 );



//////////////////////////////////////////

ambient=(0.2,0.2,0.2);

////////////////////////////

choice=2;
tchoice=1;
perm3all(a,b,c,d):=(
 (a,b,c,d),
 (a,b,d,c),
 (a,c,b,d),
 (a,c,d,b),
 (a,d,b,c),
 (a,d,c,b)
);

perm4(a,b,c,d):=
perm3all(a,b,c,d)++
perm3all(b,a,d,c)++
perm3all(c,d,a,b)++
perm3all(d,c,b,a);

perm3ev(a,b,c,d):=(
 (a,b,c,d),
 (a,c,d,b),
 (a,d,b,c)
);

perm4ev(a,b,c,d):=
perm3ev(a,b,c,d)++
perm3ev(b,a,d,c)++
perm3ev(c,d,a,b)++
perm3ev(d,c,b,a);


pm1(a,b,c,d):=(
  (a,b,c,d),
  (-a,b,c,d));

pm2(a,b,c,d):=
pm1(a,b,c,d)++pm1(a,-b,c,d);
pm3(a,b,c,d):=
pm2(a,b,c,d)++pm2(a,b,-c,d);
pm4(a,b,c,d):=
pm3(a,b,c,d)++pm3(a,b,c,-d);

tau=(sqrt(5)-1)/2;

cell5=(
  (1,1,1,0),
  (1,-1,-1,0),
  (-1,1,-1,0),
  (-1,-1,1,0),
  (0,0,0,sqrt(5))
)*1.6;




spanfactor=(
(1,1,1,1),
(1,.55,.33,.37),
(.24,.16,.16,1),
(.54,.24,.08,.37),
(.24,.16,.16,.8),
(1.85,.21,.16,.24)
);


//////////////////////////////////////////////////

b5=[[[1.6,1.6,1.6,-0.71554175279993],
[1.6,-1.6,-1.6,-0.71554175279993],
[-1.6,1.6,-1.6,-0.71554175279993],
[-1.6,-1.6,1.6,-0.71554175279993],
[0,0,0,2.86216701119973]],
[[[1.6,1.6,1.6,-0.71554175279993],
[1.6,-1.6,-1.6,-0.71554175279993]],
[[1.6,1.6,1.6,-0.71554175279993],
[-1.6,1.6,-1.6,-0.71554175279993]],
[[1.6,1.6,1.6,-0.71554175279993],
[-1.6,-1.6,1.6,-0.71554175279993]],
[[1.6,1.6,1.6,-0.71554175279993],
[0,0,0,2.86216701119973]],
[[1.6,-1.6,-1.6,-0.71554175279993],
[-1.6,1.6,-1.6,-0.71554175279993]],
[[1.6,-1.6,-1.6,-0.71554175279993],
[-1.6,-1.6,1.6,-0.71554175279993]],
[[1.6,-1.6,-1.6,-0.71554175279993],
[0,0,0,2.86216701119973]],
[[-1.6,1.6,-1.6,-0.71554175279993],
[-1.6,-1.6,1.6,-0.71554175279993]],
[[-1.6,1.6,-1.6,-0.71554175279993],
[0,0,0,2.86216701119973]],
[[-1.6,-1.6,1.6,-0.71554175279993],
[0,0,0,2.86216701119973]]],
[0,0,0,-2.86216701119973],
[1.6,1.6,-1.6,-2.1466252583998],
[3.2,0,0,-1.43108350559987],
[1.6,1.6,1.6,-0.71554175279993]] ;
b8=[[[-1.25,-1.25,-1.25,-1.25],
[-1.25,-1.25,-1.25,1.25],
[-1.25,-1.25,1.25,-1.25],
[-1.25,-1.25,1.25,1.25],
[-1.25,1.25,-1.25,-1.25],
[-1.25,1.25,-1.25,1.25],
[-1.25,1.25,1.25,-1.25],
[-1.25,1.25,1.25,1.25],
[1.25,-1.25,-1.25,-1.25],
[1.25,-1.25,-1.25,1.25],
[1.25,-1.25,1.25,-1.25],
[1.25,-1.25,1.25,1.25],
[1.25,1.25,-1.25,-1.25],
[1.25,1.25,-1.25,1.25],
[1.25,1.25,1.25,-1.25],
[1.25,1.25,1.25,1.25]],
[[[-1.25,-1.25,-1.25,-1.25],
[-1.25,-1.25,-1.25,1.25]],
[[-1.25,-1.25,-1.25,-1.25],
[-1.25,-1.25,1.25,-1.25]],
[[-1.25,-1.25,-1.25,-1.25],
[-1.25,1.25,-1.25,-1.25]],
[[-1.25,-1.25,-1.25,-1.25],
[1.25,-1.25,-1.25,-1.25]],
[[-1.25,-1.25,-1.25,1.25],
[-1.25,-1.25,-1.25,-1.25]],
[[-1.25,-1.25,-1.25,1.25],
[-1.25,-1.25,1.25,1.25]],
[[-1.25,-1.25,-1.25,1.25],
[-1.25,1.25,-1.25,1.25]],
[[-1.25,-1.25,-1.25,1.25],
[1.25,-1.25,-1.25,1.25]],
[[-1.25,-1.25,1.25,-1.25],
[-1.25,-1.25,-1.25,-1.25]],
[[-1.25,-1.25,1.25,-1.25],
[-1.25,-1.25,1.25,1.25]],
[[-1.25,-1.25,1.25,-1.25],
[-1.25,1.25,1.25,-1.25]],
[[-1.25,-1.25,1.25,-1.25],
[1.25,-1.25,1.25,-1.25]],
[[-1.25,-1.25,1.25,1.25],
[-1.25,-1.25,-1.25,1.25]],
[[-1.25,-1.25,1.25,1.25],
[-1.25,-1.25,1.25,-1.25]],
[[-1.25,-1.25,1.25,1.25],
[-1.25,1.25,1.25,1.25]],
[[-1.25,-1.25,1.25,1.25],
[1.25,-1.25,1.25,1.25]],
[[-1.25,1.25,-1.25,-1.25],
[-1.25,-1.25,-1.25,-1.25]],
[[-1.25,1.25,-1.25,-1.25],
[-1.25,1.25,-1.25,1.25]],
[[-1.25,1.25,-1.25,-1.25],
[-1.25,1.25,1.25,-1.25]],
[[-1.25,1.25,-1.25,-1.25],
[1.25,1.25,-1.25,-1.25]],
[[-1.25,1.25,-1.25,1.25],
[-1.25,-1.25,-1.25,1.25]],
[[-1.25,1.25,-1.25,1.25],
[-1.25,1.25,-1.25,-1.25]],
[[-1.25,1.25,-1.25,1.25],
[-1.25,1.25,1.25,1.25]],
[[-1.25,1.25,-1.25,1.25],
[1.25,1.25,-1.25,1.25]],
[[-1.25,1.25,1.25,-1.25],
[-1.25,-1.25,1.25,-1.25]],
[[-1.25,1.25,1.25,-1.25],
[-1.25,1.25,-1.25,-1.25]],
[[-1.25,1.25,1.25,-1.25],
[-1.25,1.25,1.25,1.25]],
[[-1.25,1.25,1.25,-1.25],
[1.25,1.25,1.25,-1.25]],
[[-1.25,1.25,1.25,1.25],
[-1.25,-1.25,1.25,1.25]],
[[-1.25,1.25,1.25,1.25],
[-1.25,1.25,-1.25,1.25]],
[[-1.25,1.25,1.25,1.25],
[-1.25,1.25,1.25,-1.25]],
[[-1.25,1.25,1.25,1.25],
[1.25,1.25,1.25,1.25]],
[[1.25,-1.25,-1.25,-1.25],
[-1.25,-1.25,-1.25,-1.25]],
[[1.25,-1.25,-1.25,-1.25],
[1.25,-1.25,-1.25,1.25]],
[[1.25,-1.25,-1.25,-1.25],
[1.25,-1.25,1.25,-1.25]],
[[1.25,-1.25,-1.25,-1.25],
[1.25,1.25,-1.25,-1.25]],
[[1.25,-1.25,-1.25,1.25],
[-1.25,-1.25,-1.25,1.25]],
[[1.25,-1.25,-1.25,1.25],
[1.25,-1.25,-1.25,-1.25]],
[[1.25,-1.25,-1.25,1.25],
[1.25,-1.25,1.25,1.25]],
[[1.25,-1.25,-1.25,1.25],
[1.25,1.25,-1.25,1.25]],
[[1.25,-1.25,1.25,-1.25],
[-1.25,-1.25,1.25,-1.25]],
[[1.25,-1.25,1.25,-1.25],
[1.25,-1.25,-1.25,-1.25]],
[[1.25,-1.25,1.25,-1.25],
[1.25,-1.25,1.25,1.25]],
[[1.25,-1.25,1.25,-1.25],
[1.25,1.25,1.25,-1.25]],
[[1.25,-1.25,1.25,1.25],
[-1.25,-1.25,1.25,1.25]],
[[1.25,-1.25,1.25,1.25],
[1.25,-1.25,-1.25,1.25]],
[[1.25,-1.25,1.25,1.25],
[1.25,-1.25,1.25,-1.25]],
[[1.25,-1.25,1.25,1.25],
[1.25,1.25,1.25,1.25]],
[[1.25,1.25,-1.25,-1.25],
[-1.25,1.25,-1.25,-1.25]],
[[1.25,1.25,-1.25,-1.25],
[1.25,-1.25,-1.25,-1.25]],
[[1.25,1.25,-1.25,-1.25],
[1.25,1.25,-1.25,1.25]],
[[1.25,1.25,-1.25,-1.25],
[1.25,1.25,1.25,-1.25]],
[[1.25,1.25,-1.25,1.25],
[-1.25,1.25,-1.25,1.25]],
[[1.25,1.25,-1.25,1.25],
[1.25,-1.25,-1.25,1.25]],
[[1.25,1.25,-1.25,1.25],
[1.25,1.25,-1.25,-1.25]],
[[1.25,1.25,-1.25,1.25],
[1.25,1.25,1.25,1.25]],
[[1.25,1.25,1.25,-1.25],
[-1.25,1.25,1.25,-1.25]],
[[1.25,1.25,1.25,-1.25],
[1.25,-1.25,1.25,-1.25]],
[[1.25,1.25,1.25,-1.25],
[1.25,1.25,-1.25,-1.25]],
[[1.25,1.25,1.25,-1.25],
[1.25,1.25,1.25,1.25]],
[[1.25,1.25,1.25,1.25],
[-1.25,1.25,1.25,1.25]],
[[1.25,1.25,1.25,1.25],
[1.25,-1.25,1.25,1.25]],
[[1.25,1.25,1.25,1.25],
[1.25,1.25,-1.25,1.25]],
[[1.25,1.25,1.25,1.25],
[1.25,1.25,1.25,-1.25]]],
[1,1,1,1],
[1,1,1,0],
[1,1,0,0],
[1,0,0,0]] ;
b16=[[[-2.5,0,0,0],
[0,-2.5,0,0],
[0,0,-2.5,0],
[0,0,0,-2.5],
[0,0,0,2.5],
[0,0,2.5,0],
[0,2.5,0,0],
[2.5,0,0,0]],
[[[-2.5,0,0,0],
[0,-2.5,0,0]],
[[-2.5,0,0,0],
[0,0,-2.5,0]],
[[-2.5,0,0,0],
[0,0,0,-2.5]],
[[-2.5,0,0,0],
[0,0,0,2.5]],
[[-2.5,0,0,0],
[0,0,2.5,0]],
[[-2.5,0,0,0],
[0,2.5,0,0]],
[[0,-2.5,0,0],
[-2.5,0,0,0]],
[[0,-2.5,0,0],
[0,0,-2.5,0]],
[[0,-2.5,0,0],
[0,0,0,-2.5]],
[[0,-2.5,0,0],
[0,0,0,2.5]],
[[0,-2.5,0,0],
[0,0,2.5,0]],
[[0,-2.5,0,0],
[2.5,0,0,0]],
[[0,0,-2.5,0],
[-2.5,0,0,0]],
[[0,0,-2.5,0],
[0,-2.5,0,0]],
[[0,0,-2.5,0],
[0,0,0,-2.5]],
[[0,0,-2.5,0],
[0,0,0,2.5]],
[[0,0,-2.5,0],
[0,2.5,0,0]],
[[0,0,-2.5,0],
[2.5,0,0,0]],
[[0,0,0,-2.5],
[-2.5,0,0,0]],
[[0,0,0,-2.5],
[0,-2.5,0,0]],
[[0,0,0,-2.5],
[0,0,-2.5,0]],
[[0,0,0,-2.5],
[0,0,2.5,0]],
[[0,0,0,-2.5],
[0,2.5,0,0]],
[[0,0,0,-2.5],
[2.5,0,0,0]],
[[0,0,0,2.5],
[-2.5,0,0,0]],
[[0,0,0,2.5],
[0,-2.5,0,0]],
[[0,0,0,2.5],
[0,0,-2.5,0]],
[[0,0,0,2.5],
[0,0,2.5,0]],
[[0,0,0,2.5],
[0,2.5,0,0]],
[[0,0,0,2.5],
[2.5,0,0,0]],
[[0,0,2.5,0],
[-2.5,0,0,0]],
[[0,0,2.5,0],
[0,-2.5,0,0]],
[[0,0,2.5,0],
[0,0,0,-2.5]],
[[0,0,2.5,0],
[0,0,0,2.5]],
[[0,0,2.5,0],
[0,2.5,0,0]],
[[0,0,2.5,0],
[2.5,0,0,0]],
[[0,2.5,0,0],
[-2.5,0,0,0]],
[[0,2.5,0,0],
[0,0,-2.5,0]],
[[0,2.5,0,0],
[0,0,0,-2.5]],
[[0,2.5,0,0],
[0,0,0,2.5]],
[[0,2.5,0,0],
[0,0,2.5,0]],
[[0,2.5,0,0],
[2.5,0,0,0]],
[[2.5,0,0,0],
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[1.15,-1.15,-1.15,-1.15]],
[[1.86073908706238,0,-0.71073908706238,-1.15],
[1.15,1.15,-1.15,-1.15]],
[[1.86073908706238,0,-0.71073908706238,-1.15],
[0.71073908706238,0,-1.15,-1.86073908706238]],
[[1.86073908706238,0,-0.71073908706238,-1.15],
[1.15,-0.71073908706238,0,-1.86073908706238]],
[[1.86073908706238,0,-0.71073908706238,-1.15],
[1.15,0,-1.86073908706238,-0.71073908706238]],
[[1.86073908706238,0,-0.71073908706238,-1.15],
[1.15,0.71073908706238,0,-1.86073908706238]],
[[1.86073908706238,0,-0.71073908706238,-1.15],
[1.86073908706238,-1.15,0,-0.71073908706238]],
[[1.86073908706238,0,-0.71073908706238,-1.15],
[1.86073908706238,-0.71073908706238,-1.15,0]],
[[1.86073908706238,0,-0.71073908706238,-1.15],
[1.86073908706238,0,0.71073908706238,-1.15]],
[[1.86073908706238,0,-0.71073908706238,-1.15],
[1.86073908706238,0.71073908706238,-1.15,0]],
[[1.86073908706238,0,-0.71073908706238,-1.15],
[1.86073908706238,1.15,0,-0.71073908706238]],
[[1.86073908706238,0,-0.71073908706238,1.15],
[2.3,0,0,0]],
[[1.86073908706238,0,-0.71073908706238,1.15],
[1.15,-1.15,-1.15,1.15]],
[[1.86073908706238,0,-0.71073908706238,1.15],
[1.15,1.15,-1.15,1.15]],
[[1.86073908706238,0,-0.71073908706238,1.15],
[0.71073908706238,0,-1.15,1.86073908706238]],
[[1.86073908706238,0,-0.71073908706238,1.15],
[1.15,-0.71073908706238,0,1.86073908706238]],
[[1.86073908706238,0,-0.71073908706238,1.15],
[1.15,0,-1.86073908706238,0.71073908706238]],
[[1.86073908706238,0,-0.71073908706238,1.15],
[1.15,0.71073908706238,0,1.86073908706238]],
[[1.86073908706238,0,-0.71073908706238,1.15],
[1.86073908706238,-1.15,0,0.71073908706238]],
[[1.86073908706238,0,-0.71073908706238,1.15],
[1.86073908706238,-0.71073908706238,-1.15,0]],
[[1.86073908706238,0,-0.71073908706238,1.15],
[1.86073908706238,0,0.71073908706238,1.15]],
[[1.86073908706238,0,-0.71073908706238,1.15],
[1.86073908706238,0.71073908706238,-1.15,0]],
[[1.86073908706238,0,-0.71073908706238,1.15],
[1.86073908706238,1.15,0,0.71073908706238]],
[[1.86073908706238,0,0.71073908706238,-1.15],
[2.3,0,0,0]],
[[1.86073908706238,0,0.71073908706238,-1.15],
[1.15,-1.15,1.15,-1.15]],
[[1.86073908706238,0,0.71073908706238,-1.15],
[1.15,1.15,1.15,-1.15]],
[[1.86073908706238,0,0.71073908706238,-1.15],
[0.71073908706238,0,1.15,-1.86073908706238]],
[[1.86073908706238,0,0.71073908706238,-1.15],
[1.15,-0.71073908706238,0,-1.86073908706238]],
[[1.86073908706238,0,0.71073908706238,-1.15],
[1.15,0,1.86073908706238,-0.71073908706238]],
[[1.86073908706238,0,0.71073908706238,-1.15],
[1.15,0.71073908706238,0,-1.86073908706238]],
[[1.86073908706238,0,0.71073908706238,-1.15],
[1.86073908706238,-1.15,0,-0.71073908706238]],
[[1.86073908706238,0,0.71073908706238,-1.15],
[1.86073908706238,-0.71073908706238,1.15,0]],
[[1.86073908706238,0,0.71073908706238,-1.15],
[1.86073908706238,0,-0.71073908706238,-1.15]],
[[1.86073908706238,0,0.71073908706238,-1.15],
[1.86073908706238,0.71073908706238,1.15,0]],
[[1.86073908706238,0,0.71073908706238,-1.15],
[1.86073908706238,1.15,0,-0.71073908706238]],
[[1.86073908706238,0,0.71073908706238,1.15],
[2.3,0,0,0]],
[[1.86073908706238,0,0.71073908706238,1.15],
[1.15,-1.15,1.15,1.15]],
[[1.86073908706238,0,0.71073908706238,1.15],
[1.15,1.15,1.15,1.15]],
[[1.86073908706238,0,0.71073908706238,1.15],
[0.71073908706238,0,1.15,1.86073908706238]],
[[1.86073908706238,0,0.71073908706238,1.15],
[1.15,-0.71073908706238,0,1.86073908706238]],
[[1.86073908706238,0,0.71073908706238,1.15],
[1.15,0,1.86073908706238,0.71073908706238]],
[[1.86073908706238,0,0.71073908706238,1.15],
[1.15,0.71073908706238,0,1.86073908706238]],
[[1.86073908706238,0,0.71073908706238,1.15],
[1.86073908706238,-1.15,0,0.71073908706238]],
[[1.86073908706238,0,0.71073908706238,1.15],
[1.86073908706238,-0.71073908706238,1.15,0]],
[[1.86073908706238,0,0.71073908706238,1.15],
[1.86073908706238,0,-0.71073908706238,1.15]],
[[1.86073908706238,0,0.71073908706238,1.15],
[1.86073908706238,0.71073908706238,1.15,0]],
[[1.86073908706238,0,0.71073908706238,1.15],
[1.86073908706238,1.15,0,0.71073908706238]],
[[1.86073908706238,0.71073908706238,-1.15,0],
[2.3,0,0,0]],
[[1.86073908706238,0.71073908706238,-1.15,0],
[1.15,1.15,-1.15,-1.15]],
[[1.86073908706238,0.71073908706238,-1.15,0],
[1.15,1.15,-1.15,1.15]],
[[1.86073908706238,0.71073908706238,-1.15,0],
[0.71073908706238,1.15,-1.86073908706238,0]],
[[1.86073908706238,0.71073908706238,-1.15,0],
[1.15,0,-1.86073908706238,-0.71073908706238]],
[[1.86073908706238,0.71073908706238,-1.15,0],
[1.15,0,-1.86073908706238,0.71073908706238]],
[[1.86073908706238,0.71073908706238,-1.15,0],
[1.15,1.86073908706238,-0.71073908706238,0]],
[[1.86073908706238,0.71073908706238,-1.15,0],
[1.86073908706238,-0.71073908706238,-1.15,0]],
[[1.86073908706238,0.71073908706238,-1.15,0],
[1.86073908706238,0,-0.71073908706238,-1.15]],
[[1.86073908706238,0.71073908706238,-1.15,0],
[1.86073908706238,0,-0.71073908706238,1.15]],
[[1.86073908706238,0.71073908706238,-1.15,0],
[1.86073908706238,1.15,0,-0.71073908706238]],
[[1.86073908706238,0.71073908706238,-1.15,0],
[1.86073908706238,1.15,0,0.71073908706238]],
[[1.86073908706238,0.71073908706238,1.15,0],
[2.3,0,0,0]],
[[1.86073908706238,0.71073908706238,1.15,0],
[1.15,1.15,1.15,-1.15]],
[[1.86073908706238,0.71073908706238,1.15,0],
[1.15,1.15,1.15,1.15]],
[[1.86073908706238,0.71073908706238,1.15,0],
[0.71073908706238,1.15,1.86073908706238,0]],
[[1.86073908706238,0.71073908706238,1.15,0],
[1.15,0,1.86073908706238,-0.71073908706238]],
[[1.86073908706238,0.71073908706238,1.15,0],
[1.15,0,1.86073908706238,0.71073908706238]],
[[1.86073908706238,0.71073908706238,1.15,0],
[1.15,1.86073908706238,0.71073908706238,0]],
[[1.86073908706238,0.71073908706238,1.15,0],
[1.86073908706238,-0.71073908706238,1.15,0]],
[[1.86073908706238,0.71073908706238,1.15,0],
[1.86073908706238,0,0.71073908706238,-1.15]],
[[1.86073908706238,0.71073908706238,1.15,0],
[1.86073908706238,0,0.71073908706238,1.15]],
[[1.86073908706238,0.71073908706238,1.15,0],
[1.86073908706238,1.15,0,-0.71073908706238]],
[[1.86073908706238,0.71073908706238,1.15,0],
[1.86073908706238,1.15,0,0.71073908706238]],
[[1.86073908706238,1.15,0,-0.71073908706238],
[2.3,0,0,0]],
[[1.86073908706238,1.15,0,-0.71073908706238],
[1.15,1.15,-1.15,-1.15]],
[[1.86073908706238,1.15,0,-0.71073908706238],
[1.15,1.15,1.15,-1.15]],
[[1.86073908706238,1.15,0,-0.71073908706238],
[0.71073908706238,1.86073908706238,0,-1.15]],
[[1.86073908706238,1.15,0,-0.71073908706238],
[1.15,0.71073908706238,0,-1.86073908706238]],
[[1.86073908706238,1.15,0,-0.71073908706238],
[1.15,1.86073908706238,-0.71073908706238,0]],
[[1.86073908706238,1.15,0,-0.71073908706238],
[1.15,1.86073908706238,0.71073908706238,0]],
[[1.86073908706238,1.15,0,-0.71073908706238],
[1.86073908706238,0,-0.71073908706238,-1.15]],
[[1.86073908706238,1.15,0,-0.71073908706238],
[1.86073908706238,0,0.71073908706238,-1.15]],
[[1.86073908706238,1.15,0,-0.71073908706238],
[1.86073908706238,0.71073908706238,-1.15,0]],
[[1.86073908706238,1.15,0,-0.71073908706238],
[1.86073908706238,0.71073908706238,1.15,0]],
[[1.86073908706238,1.15,0,-0.71073908706238],
[1.86073908706238,1.15,0,0.71073908706238]],
[[1.86073908706238,1.15,0,0.71073908706238],
[2.3,0,0,0]],
[[1.86073908706238,1.15,0,0.71073908706238],
[1.15,1.15,-1.15,1.15]],
[[1.86073908706238,1.15,0,0.71073908706238],
[1.15,1.15,1.15,1.15]],
[[1.86073908706238,1.15,0,0.71073908706238],
[0.71073908706238,1.86073908706238,0,1.15]],
[[1.86073908706238,1.15,0,0.71073908706238],
[1.15,0.71073908706238,0,1.86073908706238]],
[[1.86073908706238,1.15,0,0.71073908706238],
[1.15,1.86073908706238,-0.71073908706238,0]],
[[1.86073908706238,1.15,0,0.71073908706238],
[1.15,1.86073908706238,0.71073908706238,0]],
[[1.86073908706238,1.15,0,0.71073908706238],
[1.86073908706238,0,-0.71073908706238,1.15]],
[[1.86073908706238,1.15,0,0.71073908706238],
[1.86073908706238,0,0.71073908706238,1.15]],
[[1.86073908706238,1.15,0,0.71073908706238],
[1.86073908706238,0.71073908706238,-1.15,0]],
[[1.86073908706238,1.15,0,0.71073908706238],
[1.86073908706238,0.71073908706238,1.15,0]],
[[1.86073908706238,1.15,0,0.71073908706238],
[1.86073908706238,1.15,0,-0.71073908706238]]],
[1,0,0,0],
[1,0.61803398874989,0,0],
[1,0.38196601125011,0,0],
[1,1,0,0]] ;



        </script>

        <script id="csdraw" type="text/x-cindyscript">

        fillcircle((0,0),30,color->(0,0,0));
        repeat(36*5,w=#*2°;
           fillcircle(O+(sin(w),cos(w))*2,.2,color->hue(w/360°)*.7)
        );
        
        y=S.y;
          if(y<S1.y,y=S1.y);
          if(y>S2.y,y=S2.y);
          
          S.xy=(S1.x,y);

        s1=(|S,S1|/|S1,S2|);
        X.xy=(X-O)/|X-O|*2.3+O;
        ww=X-O;
        win1=arctan2(ww.y,ww.x);

        if(mover()==Y,
          Y.xy=(Y-O)/|Y-O|*2.3+O,
          Y.xy=(sin(win1-oldangle),cos(win1-oldangle))*2.3+O
          
        );
     

ww=Y-O;
win2=arctan2(ww.y,ww.x);
if(win2-win1>0,win2=win2-360°);
oldangle=-win2+win1;
  
     dd=|round((win2-win1)/2°)|;  
        repeat(dd,w=-#*2°;
           fillcircle(O+(sin(win1+w),cos(win1+w))*2.3,.07,color->(1,1,1))
        );    

  
if(choice==0,definebody(b5));
if(choice==1,definebody(b16));
if(choice==2,definebody(b8));
if(choice==3,definebody(b24));
if(choice==4,definebody(b120));
if(choice==5,definebody(b600));

if(tchoice==1,dir=rf1);
if(tchoice==2,dir=rf2);
if(tchoice==3,dir=rf3);
if(tchoice==4,dir=rf4);


//if(mover()==Rot,
//  Span.angle=Rot.angle+oldang;
//);


//oldang=Span.angle-Rot.angle;
//colspan=if(Span.angle<Rot.angle,oldang+2*pi,oldang);
//angle=Rot.angle;

colspan=win1-win2;
angle=win2;


colparams=(colspan,angle);

//alpha=|U,W|/|U,V|;

alpha=0.5;

col1=[0,0,1];
col2=[.1,1,0]*0;
col3=[1,0,1]*0;
actcol=(1,1,1);


col1=[.9,.9,1]*.5;
col2=[1,.9,.9]*.5;
col3=[1,1,1]*0;
actcol=(.5,.8,1);


amb=0.2;

lights=[
   [[-cos(30°),-sin(30°),-.5],col1],
   [[-cos(150°),-sin(150°),-.5],col2],
   [[-cos(270°),-sin(270°),-.5],col3]
];
ambient=(1,1,1)*amb;

//param1=|E,F|/|D,E|;

param1=s1;

paramv=(choice,tchoice,param1,colspan,angle);

v1=(1,0,0);
v2=(1,1,0);
v3=(1,0,1);

n1=nn(dir);
n2=(-n1_2,n1_1,-n1_4,n1_3);
n3=(-n1_3,n1_4,n1_1,-n1_2);
n4=(-n1_4,-n1_3,n1_2,n1_1);

//err("A2 "+seconds());

if(|paramv,oldparamv|>0.0001,

//err("recalc "+ seconds());

max=sort(apply(body,dir*#))_1; 

pts=select(body,dir*#~=max);
sp=sum(pts)/length(pts);
max=|sp|;


//initdirs berechnen
w=-max*.999;

ss=select(segs,(n1*#_1-w)*(n1*#_2-w)~<0);
ss=apply(ss,
  erg=linearsolve(((#_1*n1,#_2*n1),(1,1)),(w,1));
  erg_1*#_1+erg_2*#_2;
);

objx=apply(ss,(#*n2,#*n3,#*n4))*.5;
 ch=convexhull3d(objx);
 obj=ch_1;
 ff=ch_2;

 initdirs=apply(ff,
 linearsolve((obj_(#_1),obj_(#_2),obj_(#_3)),(1,1,1));
);

if(initdirs==[],
 initdirs=[(1,1,1)]
);


dnn=abs(reverse(sort(initdirs,|#|))_1);
initdirs=select(initdirs,|#|~=dnn);
initdirs=apply(initdirs,#/|#|);

//initdirs hier fertig

w=(param1*2-1)*max*0.999+.000001;

if(choice==0,
 if(tchoice==1,w=(w+max)*.62-max;);
 if(tchoice==2,w=(w+max)*.83-max;);
 if(tchoice==3,w=(w+max)*1.25-max;);
 if(tchoice==4,w=(w+max)*2.5-max;);
);


ss=select(segs,(n1*#_1-w)*(n1*#_2-w)~<0);
ss=apply(ss,
  erg=linearsolve(((#_1*n1,#_2*n1),(1,1)),(w,1));
  erg_1*#_1+erg_2*#_2;
);
objx=apply(ss,(#*n2,#*n3,#*n4))*.5;






 init=0;

if(length(objx)>3,



 ch=convexhull3d(objx);

 obj=ch_1;
 ff=ch_2;

 actcol=(.5,.8,1);

 ff=apply(ff,reverse(#));




 faces=apply(ff,[#,colorf(obj,#)]);

 oldparamv=paramv;

 );
  object(obj,faces);
);//End recalc

//err("A3 "+seconds());

translate((1,0));
 render3d();
translate((-1,0));
 
 
highlight(a):=(
repeat(10,i,
  fillcircle(a,-i*.1+1.9,alpha->i/10,color->(0.6,0.6,.9)*.6);
 );
);

//err("A4 "+seconds());









//fillpoly(((15,-4),(100,-4),(100,20),(15,20)),color->(0.3,0.4,0.5));

colchoice(i):=if(i==choice,(1,1,1),(1,1,1)*.5);

drawtext((15,8),"Simplex",size->14,color->colchoice(0));
drawtext((15,6.5),"Kreuzpolytop",size->14,color->colchoice(1));
drawtext((15,5),"Hyperwürfel",size->14,color->colchoice(2));
drawtext((15,3.5),"24-Zell",size->14,color->colchoice(3));
drawtext((15,2),"120-Zell",size->14,color->colchoice(4));
drawtext((15,.5),"600-Zell",size->14,color->colchoice(5));


tchoice(i):=if(i==tchoice,(1,1,1),(1,1,1)*.5);


de=2.3;
xx=15.5;
yy=1;
draw((xx,yy-3),color->tchoice(1),border->false);

xx=xx+de;
draw((xx-.5,yy-3.5),color->tchoice(2),border->false);
draw((xx+.5,yy-2.5),color->tchoice(2),border->false);
draw((xx-.5,yy-3.5),(xx+.5,yy-2.5),color->tchoice(2),border->false);

xx=xx+de;
draw((xx-.6,yy-3.5),color->tchoice(3),border->false);
draw((xx,yy-2.5),color->tchoice(3),border->false);
draw((xx+.6,yy-3.5),color->tchoice(3),border->false);

draw((xx+.6,yy-3.5),(xx-.6,yy-3.5),color->tchoice(3),border->false);
draw((xx-.6,yy-3.5),(xx,yy-2.5),color->tchoice(3),border->false);
draw((xx+.6,yy-3.5),(xx,yy-2.5),color->tchoice(3),border->false);

xx=xx+de;
aa=(xx-.6,yy-3.5);
bb=(xx+.4,yy-3.5);
cc=(xx-.4,yy-2.5);
dd=(xx+.6,yy-2.5);

draw(aa,bb,color->tchoice(4),border->false);
draw(aa,cc,color->tchoice(4),border->false);
draw(bb,cc,color->tchoice(4),border->false);
draw(bb,dd,color->tchoice(4),border->false);
draw(cc,dd,color->tchoice(4),border->false);
draw(aa,dd,color->(0,0,0),border->false,size->4);
draw(aa,dd,color->tchoice(4),border->false);

draw(aa,color->tchoice(4),border->false);
draw(bb,color->tchoice(4),border->false);
draw(cc,color->tchoice(4),border->false);
draw(dd,color->tchoice(4),border->false);




repeat(round(colspan/3°)-1,i,
  draw(
   H+(0,0.05)+|Rot-H|*(cos(i*3°+angle),sin(i*3°+angle)),
   H+(0,0.05)+|Rot-H|*(cos(i*3°+angle-3°),sin(i*3°+angle-3°)),
   color->(1,1,1),size->6);
);




        
           
            
              
        </script>
        
        
       <script id="down" type="text/x-cindyscript">

startx=mouse().x;
starty=mouse().y;
mm=mouse().xy;
dragging=mm.x<10;
        </script>

       <script id="up" type="text/x-cindyscript">

d=1.5;

if(mouse().x>15 & mouse().y>7.5  & mouse().y<8.7,choice=0);
if(mouse().x>15 & mouse().y>7.5-d  & mouse().y<8.7-d,choice=1);
if(mouse().x>15 & mouse().y>7.5-2*d  & mouse().y<8.7-2*d,choice=2);
if(mouse().x>15 & mouse().y>7.5-3*d  & mouse().y<8.7-3*d,choice=3);
if(mouse().x>15 & mouse().y>7.5-4*d  & mouse().y<8.7-4*d,choice=4);
if(mouse().x>15 & mouse().y>7.5-5*d  & mouse().y<8.7-5*d,choice=5);

de=2.3;
xx=15.5;
if(|mouse().x-xx| < 1.2 & |mouse().y+2|<1.2 ,tchoice=1);
xx=xx+de;
if(|mouse().x-xx| < 1.2 & |mouse().y+2|<1.2 ,tchoice=2);
xx=xx+de;
if(|mouse().x-xx| < 1.2 & |mouse().y+2|<1.2 ,tchoice=3);
xx=xx+de;
if(|mouse().x-xx| < 1.2 & |mouse().y+2|<1.2 ,tchoice=4);




        </script>

       <script id="drag" type="text/x-cindyscript">

if(dragging, 

xx=mouse().x;
yy=mouse().y;
wy=(startx-xx)*.3;
wx=-(starty-yy)*.3;

mmmx=[
  [1,0,0],
  [0,cos(wx),sin(wx)],
  [0,-sin(wx),cos(wx)]
];


mmmy=[
  [cos(wy),0,-sin(wy)],
  [0,1,0],
  [sin(wy),0,cos(wy)]
];



  mat=mmmx*mmmy*mat;



startx=xx;
starty=yy;



);


        </script>
        
        

        <div id="CSCanvas" style="width:800px; height:500px; border:2px solid #000000"></div>

        <script type="text/javascript">
            //defaultAppearance.clip="inci";
        //defaultAppearance.overhangLine=1.2;

            var gslp=[


                      {name:"S1", type:"Free", pos:[12,-7],color:[0,0,0],pinned:true,size:2},
    {name:"S2", type:"Free", pos:[12,8],color:[0,0,0],pinned:true,size:2},
    {name:"S", type:"Free", pos:[12,1.5],color:[1,0.5,0.5],pinned:false,size:4,narrow:true},
    {name:"l", type:"Segment", args:["S1","S2"],color:[.7,.7,.7],pinned:false,size:2},
                          {name:"O", type:"Free", pos:[18,-6],color:[0,0,0],pinned:true,size:2},
                      {name:"Ci", type:"CircleMFixedr", args:["O"],radius:1.75,color:[.7,.7,.7],size:3},
                      
                      {name:"X", type:"Free", pos:[100,-6],color:[1,1,1],size:4,narrow:true},
                      {name:"Y", type:"Free", pos:[100,-6],color:[1,1,1],size:3,narrow:true},

                      
                      ];
            CindyJS({canvasname:"CSCanvas",
                        movescript:"csdraw",
                        initscript:"init",
                        mousedownscript:"down",
                        mousedragscript:"drag",
                        mouseupscript:"up",
            language: "en",
            defaultAppearence:{},
                        geometry:gslp,
                    //    transform:[{scale:1.0},{translate:[-2,-.5]}]
                        });
    
        </script>


        
        <div style="width:800px; line-height: 1.5">
<br>        
<br>        
<br><br>
        </div>
	

        <iframe tabindex="-1" style="position: absolute; width: 0px; height: 0px; border: medium none; left: -1000px; top: -1000px;" id="quickhull3d" src="javascript:&quot;&quot;"></iframe> </body></html>
